Inverter Battery Backup: Will It Recharge Between Power Cuts?

The daily schedule repeats for seven days, beginning at midnight. The AC load is bypassed to the grid while it is available. During a cut, the assumed constant battery current is $I=(P_{AC}/\eta_{inv}+P_{idle})/V_{bank}$.

Present capacity is $C=C_{bank}f_{health}$. For lead-acid, the rated current is $I_r=C/H_r$ and Peukert's law gives the rate factor $f_r=\min[1,(I_r/I)^{k-1}]$. The full-charge discharge allowance is $D C f_r$, so its runtime is $D C f_r/I$. No capacity above the nameplate is credited below the rated current. LiFePO₄ uses $k=1$, treating its discharge capacity as approximately rate independent.

The state variable $s$ tracks physical stored Ah, rather than a Peukert-weighted charge counter. The operating cutoff is $s_c=1-Df_r$. Thus high-rate unavailable capacity remains a reserve; it is not charged again as though it had been removed. Partial discharge reduces $s$ at $I/C$ per hour. At the cutoff the inverter stops for the rest of that cut; grid return allows charging and later backup. A bank starting below cutoff cannot supply backup until it has recharged above it.

On grid, $ds/dt=\eta_c I_{ch}A(s)/C$. Acceptance is 1 below knee $b$, then $A(s)=r+(1-r)(1-s)/(1-b)$ above it. It reaches the finish-to-bulk ratio $r$ at full charge. The model integrates the constant-current and exponential taper portions exactly, caps stored charge at 100%, and discards excess charging opportunity. This adjustable acceptance law is derived here as a planning approximation, not a fitted manufacturer charge curve.

The event loop splits at every cut boundary, midnight, hour mark and discharge cutoff. Hour marks add plotting points; they are not an Euler integration time step. Uncovered time includes fractional hours after cutoff. Charge actually stored and charge actually removed are accumulated separately and checked against $C(s-s_0)$. Charts join the exact sampled states with straight segments; the animated state uses the analytic update within each segment.

The best-case daily surplus is $\eta_c I_{ch}H_{grid}-I H_{cut}$ before taper or full-charge curtailment. The cutoff-to-full time uses the same acceptance law with uninterrupted grid. Peukert examples and Ah efficiency are checked against the attached Victron manual, PDF pages 48–49 and 34; the ideal one-discharge limit is also checked against Luminous.

• Constant essential AC real power, constant nominal battery voltage and fixed inverter efficiency. The separate idle draw applies only while backup is operating.
• The charger current is net DC current available to the entire bank. Grid power supplies the AC load directly; shared mains limits must already be reflected in this current.
• The initial charge is specified at midnight before day 1. No solar input, generator, self-discharge or extra DC loads are included.
• Lead-acid defaults: C20 rating, Peukert exponent 1.25, 50% allowed discharge and 95% Ah charging efficiency. The exponent and efficiency are illustrative Victron monitor settings, not specifications for every battery.
• LiFePO₄ defaults: 80% allowed discharge, 99% Ah charging efficiency and no rate penalty. A compatible charger and BMS are assumed; BMS current and voltage limits are outside the model.
• Taper knees of 0.85 for lead-acid and 0.95 for LiFePO₄, and finish/bulk current ratio 0.15, are author-selected approximations. Change them to match measured acceptance; they are not manufacturer recommendations.
• Allowed discharge is applied to rate-adjusted available capacity. The displayed operating cutoff therefore includes a Peukert reserve and can exceed the nominal reserve $1-D$.
• Remaining capacity is a uniform derating. Temperature, resistance growth, recovery after rest and cycle ageing are not modelled.

Use for comparative planning of small inverter/IPS battery banks under a known repeating daily schedule. The seven-day forecast is conditional on the load, current and schedule; a successful day 3 is not a claim of steady operation or battery life.

Peukert is an empirical constant-current approximation. At extreme discharge rates, low temperature or near low-voltage shutdown, measured runtime may be shorter. This tool does not solve a Shepherd terminal-voltage model or select inverter/BMS cutout voltages. Use discharge curves and measured charging records for final design.

The taper model does not reproduce charger absorption timers, equalization, cell balancing, low-temperature charge blocking, charge-voltage compensation or state-of-health changes. Trojan's charging guidance establishes why bulk current cannot be assumed throughout recharge; the adjustable taper here is not a reproduction of that manufacturer's curve. Follow the specific battery's permitted current, voltage and temperature range.

No surge, VA rating, cabling, fuse, earthing, transfer-switch or installation sizing is performed. Installation work belongs to a qualified person.